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The Nonabelian Simple Groups $G, |G| < 10^6$--Minimal Generating Pairs

John McKay and Kiang-Chuen Young
Mathematics of Computation
Vol. 33, No. 146 (Apr., 1979), pp. 812-814+s1-s18
DOI: 10.2307/2006317
Stable URL: http://www.jstor.org/stable/2006317
Page Count: 21
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The Nonabelian Simple Groups $G, |G| < 10^6$--Minimal Generating Pairs
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Abstract

Minimal $(k, m, n)$ generating pairs and their associated presentations are defined for all nonabelian simple groups $G, |G| < 10^6$, excepting the family $\mathrm{PSL}(2, q)$. A complete set of minimal $(2, m, n)$ generating permutations of minimal degree is tabulated for these $G$. The set is complete in the sense that any minimal generating pair for $G$ will satisfy the same presentation as exactly one of the listed pairs.

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